Capítulo 2: Marco Teórico
2.3 Definición de términos básicos
SH2.1 Design criteria. For design temperatures at which the nominal design strength is governed by one of the two short-term mechanical properties Re(T)and Rm, the following design criteria shall be applied:
(a) Gross plastic deformation. There should be the same theoretical margin against gross plastic deformation for all design details as that provided against gross plastic deformation in major membrane areas. For this purpose, the required margin against gross plastic deformation may be assumed to be Re(T)/f for materials covered in Table S3.3.1. For other materials the value of the nearest equivalent material in Table S3.3.1 should be assumed.
(b) Incremental collapse. The stress systems imposed shall shakedown to elastic action within the first few operating cycles. The operating loads to be considered include pressure and simultaneous loadings of types listed in Clause S3.2.3 including thermal stresses.
(c) Buckling. For components or loadings associated with substantial compressive stresses, buckling shall not occur under a combined load less than twice the design combined load, at design temperature*. The design is to include pressure and simultaneous loadings of types given in Clause S3.2.3.
The design shall also take into consideration all permissible fabrication imperfections.
(d) Fatigue. The need, or otherwise, for a fatigue analysis shall be determined in accordance with Clauses S3.1.5.4 to S3.1.5.7.
SH2.2 Design acceptability. The results of experimental or theoretical investigations shall be employed to demonstrate the conformity of a design with the criteria of Paragraph SH2.1.
Local stresses in the vicinity of attachments, supports, etc, may be deemed acceptable if they comply with the requirements of Paragraph SH2.3.
In the establishing of compliance with Paragraph SH2.1(a), investigations should take account of plastic behaviour. If the theory of plastic limit analysis is employed, the limit load may be taken as the load that produces gross plastic deformation, although this may be a conservative estimate. Where it is impracticable to perform a plastic analysis, an elastic analysis may be employed as detailed in Paragraph SH3.4; alternatively, strain measurements may be made on the actual vessel during pressure and load tests.
In the establishing of compliance with Paragraph SH2.1(b), a shake-down analysis should preferably be performed; alternatively, an elastic analysis may be employed as detailed in Paragraph SH2.3.
SH2.3 Specific criteria for local stresses in vicinity of attachments, supports, etc.
Elastically calculated stresses due to local loads at attachments, supports, etc, may be deemed acceptable provided that —
(a) they occur in areas at a distance not less than 2.5 (Rt) from shell discontinuities and have a dimension in the circumferential direction not greater than one-third of the shell circumference;
* Care is to be taken under test conditi ons to avoid buckling.
(b) the direct stress intensity under relevant conditions of local loading does not exceed f or 1.2f as permitted in Table S3.1.5; and
(c) the stress intensity due to the sum of direct and bending stresses does not exceed 2f.
For nozzles and openings such stresses may be deemed acceptable provided that — (i) a nozzle or opening is not less than 2.5 (Rt) from other shell discontinuities;
(ii) the nozzle or opening is reinforced in accordance with Clause 3.19; and
(iii) the maximum surface stress calculated for the gross structural discontinuity does not exceed 2.25f.
Where significant compressive stresses are present, the possibility of buckling should be investigated and the design modified if necessary (see Paragraph SH2.1(c)).
In cases where external load is highly localized, an acceptable procedure should be to limit the algebraic sum of all stresses acting at the point to 0.9 of the specified minimum yield stress of the material.
Where only shear stress is present, it should not exceed 0.5f.
The maximum permissible bearing stresses should not exceed 1.5f.
SH2.4 Specific criteria for general application.
SH2.4.1 General. Paragraphs SH2.4.2 to SH2.4.5 provide the criteria for acceptability of design on the basis of elastic stress analysis. The analysis should take account of gross structural discontinuities, e.g. nozzles, changes in shell curvature, but not of local stress concentrations due to changes in profile such as fillet welds.
The rules require the calculated stresses to be grouped in five stress categories (see Paragraph SH2.4.3) and appropriate stress intensities fm, fL, fb, fg, and fpto be determined from the principal stresses f1, f2, and f3in each category, in accordance with the maximum shear theory of failure. Appropriate stress limits are given for the stress intensity so calculated.
SH2.4.2 Terms relating to stress analysis. Terms used in this Appendix relating to stress analysis are defined as follows:
(a) Stress intensity — twice the maximum shear stress. In other words, the stress intensity is the difference between the algebraically largest principal stress and the algebraically smallest principal stress at a given point. Tension stresses are considered positive and compression stresses are considered negative.
(b) Gross structural discontinuity — a source of stress or strain intensification which affects a relatively large portion of a vessel and which has a significant effect on the overall stress or strain pattern or has a significant effect on the vessel as a whole.
Examples of gross structural discontinuities are head-to-shell and flange-to-shell junctions, nozzles and junctions between shells of different diameters or thicknesses.
(c) Local structural discontinuity — source of stress or strain intensification which affects a relatively small volume of material but which does not have a significant effect on the overall stress or strain pattern or on the structure as a whole.
Examples of local structural discontinuities are small fillet radii, small attachments and partial penetration welds.
(d) Normal stress — the component of stress normal to the plane of reference. (This is also referred to as ‘direct stress’.)
Usually the distribution of normal stress is not uniform through the thickness of a part, so this stress is considered to be made up in turn of two components, one of which is uniformly distributed and equal to the average value of stress across the thickness of the section under consideration and the other of which varies with the location across the thickness.
(e) Shear stress — the components of stress tangent to the plane of reference.
(f) Membrane stress — the component of normal stress which is uniformly distributed and equal to the average value of stress across the thickness of the section under consideration.
(g) Primary stress — a stress produced by mechanical loadings only and which is so distributed in the structure that no redistribution of load occurs as a result of yielding.
It is a normal stress or a shear stress developed by the imposed loading which is necessary to satisfy the simple laws of equilibrium of external and internal forces and moments. Primary stresses that considerably exceed the yield stress will result in failure, or at least in gross distortion. A thermal stress is not classified as a primary stress. Primary stress is divided into ‘general’ and ‘local’ categories. The local primary stress is defined in (h) below.
Examples of general primary stresses are —
(i) the stress in a circular, cylindrical or spherical shell due to internal pressure or to distributed live loads; and
(ii) bending stress in the central portion of a flat head due to pressure.
(h) Local primary stress — cases arise in which a membrane stress produced by pressure or other mechanical loading and associated with a primary or a discontinuity effect or both, produces excessive distortion in the transfer of load to other portions of the structure. Conservatism requires that such a stress be classified as a local primary membrane stress even though it has some characteristics of a secondary stress. A stressed region may be considered as local if the distance over which the stress intensity exceeds 1.1f does not extend in the meridional direction more than 0.5 (Rt) and if it is not closer in the meridional direction than 2.5 (Rt) to another region where the limits of general primary membrane stress are exceeded. (R is the distance measured along the perpendicular to the surface from the axis of revolution of the vessel to the midsurface of the vessel; t is the wall thickness at the location where the general primary membrane stress limit is exceeded.)
An example of a primary local stress is the membrane stress in a shell produced by external load and moment at permanent support or at a nozzle connection.
(i) Secondary stress — a normal stress or a shear stress developed by the constraint of adjacent parts or by self-constraint of a structure. The basic characteristic of a secondary stress is that it is self-limiting. Local yielding and minor distortions can satisfy the conditions which cause the stress to occur, and failure from one application of the stress is not to be expected.
An example of secondary stress is bending stress at a gross structural discontinuity.
(j) Peak stress — the basic characteristic of a peak stress is that it does not cause any noticeable distortion and is objectionable only as a possible source of a fatigue crack or a brittle fracture. A stress which is not highly localized falls into this category if it is of a type which cannot cause noticeable distortion.
Examples of peak stress are —
(i) the thermal stress in the austenitic steel cladding of a carbon steel vessel;
(ii) the surface stresses in the wall of a vessel or pipe produced by thermal shock;
and
(iii) the stress at a local structural discontinuity.
SH2.4.3 Stress categories and stress limits. A calculated stress depending upon the type of loading or the distribution of such stress will fall within one of the five basic stress categories defined below. For each category, a stress intensity value is derived for a specific condition of design. This stress intensity, to satisfy the analysis, should fall within the limit specified in each category. The limits are summarized in Figure SH2.4.3.
(a) General primary membrane stress category — the stresses falling within this category are those defined as general primary stresses in Paragraph SH2.4.2(g) and are produced by pressure and mechanical loads, but exclude all secondary and peak stresses. The value of the membrane stress intensity is obtained by averaging these stresses across the thickness of the section under consideration. The limiting value of this stress intensity (fm) is kf, using values of k as permitted in Table S3.1.5.
(b) Local primary membrane stress category — the stresses falling within this category are those defined in Paragraph SH2.4.2(h) and are produced by pressure and mechanical loads, but exclude all thermal and peak stresses. The stress intensity (fL) is the average value of these stresses across the thickness of the section under consideration and is limited to 1.5kf.
(c) General or local primary membrane plus primary bending stress category — the stresses falling within this category are those defined in Paragraph SH2.4.2(g), but the stress intensity value [(fb), (fm + fb), or (fL + fb)] is the highest value of those stresses acting across the section under consideration excluding secondary and peak stresses.
fbis the primary bending stress intensity, which means the component of primary stress proportional to the distance from the centroid of the solid section. The stress intensity [(fb), (fm+ fb), or (fL+ fb)] is limited to 1.5kf.
(d) Primary plus secondary stress category — the stresses falling within this category are those defined in Paragraph SH2.4.2(g) plus those of Paragraph SH2.4.2(j) produced by pressure, mechanical loads and general thermal effects. The effects of gross structural discontinuities but not of local structural discontinuities (stress concentrations) should be included. The stress intensity value [(fm + fb+ fg) or (fL + fb + fg)] is the highest value of these stresses acting across the section under consideration and is to be limited to 3.0kf (see also Note 1 of Figure SH2.4.3).
(e) Peak stress category — the stresses falling within this category are a combination of all primary, secondary and peak stresses produced by specified operating pressures and mechanical loads and by general and local thermal effects, including the effects of gross and local structural discontinuities. The stress intensity is the highest value of these stresses acting at any point across the thickness of the section under consideration. The allowable value of this stress intensity is dependent on the range of the stress difference from which it is derived and on the number of times it is to be applied. The stress intensity is to be compared with the allowable value obtained by the methods of analysis for cyclic operation when fatigue analysis is required according to Appendix SC.
Figure SH2.4.3 and Table SH2.4.3 have been included to guide the designer in establishing stress categories for some typical cases and stress intensity limits for combinations of stress categories. There will be instances when reference to definitions of stresses will be necessary to classify a specific stress condition to a stress category.
Item (f) below explains the reason for separating them into two categories ‘general’ and
‘secondary’.
(f) Thermal stress — a self-balancing stress produced by a non-uniform distribution of temperature or by differing thermal coefficients of expansion. Thermal stress is developed in a solid body whenever a volume of material is prevented from assuming the size and shape that it normally should under a change in temperature.
For the purpose of establishing allowable stresses, two types of thermal stress are recognized, depending on the volume or area in which distortion takes place, as follows:
(i) General thermal stress is associated with distortion of the structure in which it occurs. If a stress of this type, neglecting stress concentrations, exceeds twice the yield strength of the material, the elastic analysis may be invalid and successive thermal cycles may produce incremental distortion. Therefore, this type is classified as secondary stress in Table SH2.4.3 and Figure SH2.4.3.
Examples of general thermal stress are —
(A) stress produced by an axial thermal gradient in a cylindrical shell; and (B) stress produced by the temperature difference between a nozzle and the
shell to which it is attached.
(ii) Local thermal stress which is associated with almost complete suppression of the differential expansion and thus produces no significant distortion. Such stresses shall be considered only from the fatigue standpoint and are therefore classified as peak stresses in Table SH2.4.3 and Figure SH2.4.3.
Examples of local thermal stress are —
(A) the stress in a small hot spot in a vessel wall;
(B) stress from a radial temperature gradient in a cylindrical shell; and (C) the thermal stress in a cladding material which has a coefficient of
expansion different from that of the base metal.
SH2.4.4 Value of Poisson ratio. The value of Poisson ratio shall be determined as follows:
(a) In the evaluation of stresses for comparison with any stress limits other than those allowable under fatigue conditions, stresses shall be calculated on an elastic basis using the elastic value of Poisson ratio.
(b) In the evaluation of stresses for comparison with the allowable stress limits associated with fatigue conditions, the elastic equations shall be used, except that the numerical value substituted for Poisson ratio should be determined from the following equation:
ν= 0.5 - 0.2 ≥0.3
where
fy = yield strength of the material at the mean value of the temperature of the cycle
Sa = value obtained from the applicable design fatigue curve (Appendix SC, Figures SC1.2.1 and SC1.2.2) for the specific number of cycles of the condition being considered
SH2.4.5 Triaxial stresses. The algebraic sum of the three principal stresses (σ1+σ2+σ3) in any category shall not exceed 3.75f.
SH3 CREEP CONDITIONS. Comprehensive design criteria for components in the creep range are not yet available. In the meantime, the requirements of Section 3 may be used.
TABLE SH2.4.3